The biggest problem I find with the fine-tuned argument is that it is incompatible with dualism, and therefore Christianity.
Ask someone who uses it what they mean by “life” and they’ll tell you that they mean physical, intelligent life, yet they simultaneously believe that they will exist forever, along with their intelligence, in some non-physical ether. So actually, they don’t believe there is anything intelligent about physical life, infact they believe life can exist dis-embodied, which, if you follow the reasoning, would mean that nothing physical is living. A human body, for example, is a corpse that is animated by the “soul” – the essence of life, which carries on it’s existence when it leaves the physical form.
It’s not the universe that is fine-tuned for life, it’s heaven that is.
I like it. It throws the argument back at Christians.
For a previous critique of the FTA, see the link above.